Research ArticleOptimal Pipe Size Design for Looped Irrigation Water SupplySystem Using Harmony Search Saemangeum Project Area
Do Guen Yoo Ho Min Lee Ali Sadollah and Joong Hoon Kim
School of Civil Environmental and Architectural Engineering Korea University Seoul 136-713 Republic of Korea
Correspondence should be addressed to Joong Hoon Kim jaykimkoreaackr
Received 27 August 2014 Accepted 23 October 2014
Academic Editor Siamak Talatahari
Copyright copy 2015 Do Guen Yoo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Water supply systems are mainly classified into branched and looped network systems The main difference between these twosystems is that in a branched network system the flow within each pipe is a known value whereas in a looped network systemthe flow in each pipe is considered an unknown value Therefore an analysis of a looped network system is a more complex taskThis study aims to develop a technique for estimating the optimal pipe diameter for a looped agricultural irrigation water supplysystem using a harmony search algorithm which is an optimization technique This study mainly serves two purposes The first isto develop an algorithm and a program for estimating a cost-effective pipe diameter for agricultural irrigation water supply systemsusing optimization techniques The second is to validate the developed program by applying the proposed optimized cost-effectivepipe diameter to an actual study region (Saemangeum project area zone 6) The results suggest that the optimal design programwhich applies an optimization theory and enhances user convenience can be effectively applied for the real systems of a loopedagricultural irrigation water supply
1 Introduction
Water supply systems are mainly classified into branched andlooped network systems The main difference between thetwo is that in a branched network system the flow withineach pipe is a known value whereas in a looped networksystem the flow within each pipe is considered an unknownvalue Therefore an analysis of a looped network system canbe a more complex endeavor
Water supply systems form part of a larger social infras-tructure of an industrial society their objective is the effectivesupply of water from a water source to an area in demandThe analysis of a water supply system can be one of the morecomplexmathematical problems A significant fraction of theentire set of equations consists of nonlinear equations and alarge number of these equations must be solved simultane-ously
This process requires sufficient consideration of the lawof conservation of energy and a continuity equation of massIn this regard over the past few decades many methods havebeen developed to analyze water supply systems and perform
hydraulic simulations of their steady state conditions Com-mercial hydraulic analysis programs such as EPANET [1] andWaterGEMS [2] have been developed to analyze the hydraulicsimulations of large water supply systems an achievementthat could not even be dreamed of in past years
The development of suchmodels has played an importantrole in the design and operation of water supply systemsHowever problems related to the selection of the pipediameter for configuring low-cost water supply systems haveemerged as important issues that need to be resolved
In recent years many optimization methods have beenused for the design of low-cost water supply systems Theprocess for obtaining an optimal water supply system andpipe diameter is considered important because it helps indetermining the final operational costs However because theaforementioned problems are extremely complex they areconstrained by the types of methods selected for defining theproblems as well as by analysis methods thus far only amin-imization of the construction costs has been experimentallyapplied [3ndash6]
Hindawi Publishing Corporatione Scientific World JournalVolume 2015 Article ID 651763 10 pageshttpdxdoiorg1011552015651763
2 The Scientific World Journal
If the structure of a water supply system and its con-straints (water pressure and velocity) are known the optimaldesign of thewater supply system can be expressed in terms ofthe selection of a pipe diameter that minimizes the total costThe mathematical optimization methods described earliercan easily be used to find the optimal solutions in smallsystems within an ideal environment
However if existing mathematical optimization methodsare applied to actual civil engineering problems the limita-tions of these methods are revealed For example in linearprogramming because all functions applied to such problemsare linear simplified assumptions lower the accuracy of thefinal solution On the other hand in dynamic programmingtoo many combinations have to be considered to obtain theoptimal solutions thereby requiring a considerable amountof computational effort and storage space
In nonlinear programming if the initial solution is notlocated at a good position within the solution zone the globaloptimum is unobtainable and the initial solution cannotescape from the local optima To overcome these disadvan-tages during the last 20 years researchers have attempted toapply new approaches to optimization technologies that donot use an existing mathematical methodology
Rather than relying completely on conventional differen-tial derivatives the technologies currently being developedapply a natural evolution phenomenon that is the principleof the survival of the fittest and artificial imitations of thisphenomena in the optimal system design these have yieldedbetter results than those obtained using an existing optimalmathematical design
Such nature-inspired optimization algorithms are calledmetaheuristic algorithms Some examples of such algorithmsinclude a Genetic Algorithm (GA) Simulated Annealing(SA) Tabu Search (TS) Ant Colony Optimization (ACO)Harmony Search (HS) and Particle Swarm Optimization(PSO) Reca et al [7] Monem and Namdarian [8] daConceicao Cunha and Ribeiro [9] Zecchin et al [10] Geemet al [11] and Montalvo et al [12] have conducted studieson the optimal design of water supply systems using the GASA TS ACOHS and PSO algorithms respectively In recentyears hybrid versions of existing algorithms and new algo-rithms have been also developed such as Genetic HeritageEvolution by Stochastic Transmission (GHEST [13]) NLP-Differential Evolution algorithm (Combined NLP-DE [14])Hybrid Particle Swarm Optimization and Differential Evo-lution (Hybrid PSO-DE [15]) and Charged System Searchalgorithm (CSS [16])
However most of these studies have disadvantages in thatthey were applied to small benchmark problems and werenot reflected in the actual plans [17] The present study aimsto develop an optimal pipe diameter estimation technique ofan actual agricultural looped irrigation water supply systemusing an HS algorithm This study has two main purposesThe first is to develop an economic pipe diameter estimationalgorithm and programusing the optimization techniques foragricultural irrigation water supply systems The second isto validate the developed program by applying the proposedoptimized economic pipe diameter to an actual target region(Saemangeum business area zone 6)
Table 1 Land use divisions according to the comprehensive Sae-mangeum development plan
The Saemangeum Project is a reclamation project intendedto create land from a mud flat and sea waters along thewestern coast of South Korea by constructing a 339 km longseawall Under the Saemangeum Project which was startedon November 16 1991 the construction of a cofferdam wascompleted on April 21 2006 and the reinforcement andembankment projects were completed on April 27 2010
TheSaemangeumseawall is listed in theGuinness Book ofWorld Records as the longest seawall on record and is 14 kmlonger than the Zuider seawall (325 km) of the Netherlandswhichwas earlier regarded to be the longestThe constructionof the seawall has resulted in the reclamation of a new regionwith an area of 401 km2 of which land and a fresh water lakeaccount for 283 km2 and 118 km2 respectively
Upon completion of the seawall construction the SouthKorean Government newly formulated its ComprehensiveSaemangeum Development Plan According to this plan thereclaimed land is to be developed as the central agriculturaland economic sector of Northeast Asia with the reclaimedland mainly divided into nine areas as shown in Figure 1 andTable 1
Agricultural lands account for the largest share (303)among the divided areas These agricultural lands are usedfor ensuring national competitiveness producing high-value-added agricultural products and developing food-industryfacilities through mixed environment-friendly agricultureand ecological crop cultivation Traditionally agriculturalirrigation water supply systems have been designed asbranched water supply networks which incur less initialcosts However such networks are disadvantageous in thatthey do not ensure the reliability of the water supply
In recent years new cultivation methods such as green-house crop cultivation high-value-added crop cultivationand perennial cultivation have been adopted Accordinglyagricultural irrigation water supply systems also need to pro-vide a stable and reliable water supply as achieved by urbanwater supply systems
Figure 1 Comprehensive Saemangeum development plan
3 Model Development and Methodology
31 Harmony Search Algorithm The HS algorithm proposedby Geem et al [11] is an optimization technique used in pipedesign HS is a solution-finding technique that considers anoptimal solution in engineering to correspond to an optimalsound in music Generally heuristic search methods involvethe observation of natural phenomena but the HS method isan algorithmbased on the artificial phenomenon of harmony
When sounds are produced by various sources theytogether create a single harmony Some of these createdharmonies sound pleasant whereas others sound dissonantEventually the discordant harmonies disappear throughpractice and among the more appropriate harmonies (localoptimum) those that are aesthetically the most beautiful(global optimum) are achieved
In other words the HS algorithm considers an optimalsolution to be an optimal harmony found through practiceThe principle of the HS algorithm can be explained indetail by first comparing how music improvisation andoptimization calculations correspond to each other
Improvisation is the spontaneous creation of notes byperformers without relying on sheet music (score) Theability of the performers improves the more they performtogether and ultimately a top-level harmony is created Insuch an improvisation each performer (eg a saxophonistguitarist and double bass player as shown in Figure 2) canbe referred to as a decision variable or design variable (120594
1 1205942
and 1205943in Figure 2)
The musical range of each instrument (in the case of thesaxophonist eg one of the notes among Do Re and Mi
can be created) made by the corresponding performer canbe referred to as the range of each variable (in the case of 120594
1
in Figure 2 its pipe diameter may be 100 200 or 300mm)Moreover when each performer plays a different note theharmony they create (eg the harmony in the figure) (iesaxophone Do double bass Mi and guitar Sol) correspondsto the overall solution vector obtained (the solution vector forFigure 2 is 120594
1= 100mm 120594
2= 300mm and 120594
3= 500mm)
by substituting the value of each variableWhether the harmony played at a point in time is of
high quality is judged aesthetically by the performers oraudience through auditory stimuli If the harmony is verypleasant for the performers or audience it will often bereplayed in the memories Likewise during an optimizationwhether a solution vector is good or bad can be determined bysubstituting the vector in an objective function if this yieldsa better functional value than the existing one the solutionvector will be preserved
Moreover in an improvisation as the performance isrepeated better harmonies are created and ultimately ahigh level of ability is reached likewise in an optimizationoperation as additional iterations are carried out betterfunctional values are increasingly developed and ultimatelythe optimum value is obtained
The harmony memory (HM) harmony memory con-sidering rate (HMCR) and pitch adjustment rate (PAR)are important factors in the HS method for finding anoptimal solution First each musical performer should havea memory space to preserve a good harmony before startingthe important process of the HS algorithm a harmony
4 The Scientific World Journal
bullbullbull
bullbullbull
bullbullbull
100mm200mm300mm
300mm400mm500mm
500mm600mm700mm
Do Re Mi Mi Fa Sol Sol La Si
x1 x2 x3
f(100 300 500)
Figure 2 Concepts of a harmony search
BeginObjective function 119891(119909) 119909 = (119909
1 1199092 119909
119889)119879
Generate initial harmonics (Define Harmony Memory and Size HM amp HMS)Define pitch adjusting rate (PAR) pitch limits and bandwidth (BW)Define harmony memory considering rate (HMCR)while (119905 lt 119872119886119909 number of iterations)Generate new harmonics by accepting best harmonicsAdjust pitch to get new harmonics (solutions)if (119903119886119899119889 gt 119867119872119862119877) choose an existing harmonic randomlyelse if (119903119886119899119889 gt 119875119860119877) adjust the pitch randomly within limitselse generate new harmonics via randomizationend ifAccept the new harmonics (solutions) if betterend whileFind the current best solutionsEnd
Pseudocode 1 Pseudocode of HS
memory space is created by consolidating existing memoryspaces
This is called the HM and the maximum number ofharmonies that can be stored in this storage space is calledthe harmony memory size (HMS) Next to produce bettersolutions from the harmony storage space which is initiallyfilled by as many random vectors as the HMS the HSalgorithm employs three types of operators
311 Random Selection In the random selection techniquethe value of a variable is randomly selected from all values ofthe playable note range If119870 is the total number of all possiblevariable values one of them is randomly selected and theprobability of this technique being adopted is 1-HMCR
312 Memory Consideration The memory considerationtechnique picks the value of a variable from the existing high-quality notes In other words a single value is picked fromall values possessed by a variable within the storage space
Its probability is HMCR and although it can have a valuebetween 0 and 1 a value between 07 and 095 is usually usednevertheless the value is changeable
313 Pitch Adjustment For a pitch adjustment a noteobtained through a memory recall technique is considereda basic note and its pitch is trimmed by adjusting the notebased on the surrounding upper and lower notes In an actualcalculation when a single value is obtained using a memoryrecall technique it is adjusted by a one-step higher or lowervalue The PAR is the probability of this technique actuallybeing applied and it can attain a value between 0 and 1Generally the PAR has a value of around 001 to 03 butthis can vary Pseudocode 1 shows the pseudocode of the HSalgorithm
32 Objective Function An objective functionminimizes thedesign cost of an irrigation system The algorithm devel-oped in the present study was applied to an optimization
The Scientific World Journal 5
Figure 3 A looped water supply network applied to the target zone of Saemangeum
the construction costs pipe material costs and maintenancecosts are considered as the design costs according to the pipediameterTherefore the equation for the objective function isas follows
where 119862119862(119863119894) is cost function (construction cost) per unit
length (m) for each pipe diameter 119862119872(119863119894) is cost function
(maintenance cost) per unit length (m) for each pipe diam-eter 119862
119875(119863119894) is cost function (pipe material cost) per unit
length (m) for each pipe diameter 119871119894is length of the pipe (m)
119863119894is pipe diameter (mm) and119873 is total number of pipesHydraulic constraint equations are considered in opti-
mization problems Therefore a penalty function method isintroduced to convert the optimization problem subject toconstraint conditions into an optimization that is free fromthe constraint conditionsThe final objective function whichis applied using a penalty function can be defined as follows
10038161003816100381610038161003816ℎ119895minus ℎmin or max
10038161003816100381610038161003816
+
119873
sum
119894=1
119875119894
1003816100381610038161003816V119894 minus Vmin or max1003816100381610038161003816
(2)
where ℎ119895is pressure head of each node (m) ℎmin is minimum
pressure head (m) ℎmax is maximum pressure head (m) V119894
is velocity of each pipe (ms) Vmin is minimum pipe velocity(ms) Vmax is maximum pipe velocity (ms) 119875
119895 119875119894are penalty
functionswith regard to the pressure and pipe velocity and119872is total number of nodes
The above penalty function is applied only when thepressure of each node and the velocity of the pipe exceedeither the minimum or maximum value the equation belowrepresents the penalty function equation applied to the
present model In the target water supply system the mini-mum and maximum nodal pressures were set to 10 and 35mrespectively and the minimum andmaximum pipe velocitieswere set to 001 and 25ms respectively
119875119895= 120572 (10038161003816100381610038161003816ℎ119895minus ℎmin or ℎmax minus ℎ119895
10038161003816100381610038161003816) + 120573
119875119894= 120572 (1003816100381610038161003816V119894 minus Vmin or Vmax minus V119894
1003816100381610038161003816) + 120573
(3)
where 120572 120573 are penalty constantsWhen running an optimization model if the pressure
head of each node and the velocity of the pipe do notsatisfy the minimum and maximum values which are thedesign conditions the penalty cost is increased by assigninga significantly greater value to 120572 so that the solution willnot be selected To prepare for a case in which the pressurehead and pipe velocity fall short of the design conditions bya small margin a model that largely satisfies all of the designconditions was implemented by assigning a large value to 120573A trial-and-error analysis was conducted using the 120572 and 120573values for Saemangeumwhich is the target area of the presentproject The results indicate that an effective optimal designis possible when 120572 and 120573 are assigned values of 10000000and 100000000 respectively But detailed studies aboutconstraint handling techniques and determination of theirparameters should be tackled to improve model efficiencyand reliability in future
4 Saemangeum Water Supply NetworkApplication and Results
41 Target Water Supply Network In the present studyproposal data on the loop-type design of the six zones ofSaemangeum were obtained and applied to one of the zonesA diagram of the corresponding water supply network isshown in Figure 3The targetwater supply network comprises356 pipelines and as mentioned earlier some of the networkconsists of a circuit-type water supply
The data on the cost incurred per unit of pipe length forthe different diameter pipes used in this study are listed inTable 2 For optimization 18 types of commercial pipes with
6 The Scientific World Journal
Table 2 Cost data corresponding to different pipe diameters for Saemangeum
Pipe diameter (mm) Cost (xm)Construction costs Material costs Maintenance costs
Table 3 Decision variables and number of possible solutions for the target water supply network
Target water supply network Number of water supply networkdecision variables in the initial design Total length of the pipeline Number of
possible solutionsSix zones of Saemangeum(loop type) 356 40440m 18356 ≒ infin
different diameters were considered Data on the construc-tion and pipe material costs corresponding to the differentpipe diameters were obtained from the ldquoWater FacilitiesConstruction Cost Estimation Reportrdquo from K-water [18]which provides estimated data on the construction costs fordifferent steel pipe diameters The task of optimization wascarried out on Intel(R) Core(TM) i5-3570 CPU at 34GHzwith 4GBRAM EPANET [1] was used as a hydraulic analysisprogram
42 Parameter Settings The number of decision variableswhich should be determined through optimization is 356because there are 356 pipelines in the target water supplynetwork As indicated in Table 2 18 pipe diameters wereconsidered for the target water supply network Hence thenumber of possible solutions that can be considered duringthe design period is infinite as mentioned in Table 3
The parameters applied in the present program forthe Saemangeum target water supply network are listed inTable 4 The size of the harmony memory (HMS) the valueof the HMCR parameter and the value of PAR were set to 30097 and 001 respectively
These values which correspond to the optimum resultsare adjusted therefore the convergence time and efficiencyof the optimal solution vary However when there are many
Table 4 Cost data based on pipe diameters as applied to Saeman-geum
Control parameters Set valueHMS 30HMCR 097PAR 001Constraint condition (pressure ℎ) 10 lt ℎ lt 35
Constraint condition (pipe velocity V) 001 lt V lt 25
decision variables and in such a case if large HMCR andsmall PAR values are used the efficiency of the optimizationgenerally increases
43 The Economic Feasibility of the Initial Design andHydraulic Analysis Evaluation To compare and evaluate theoptimization results of the pipe diameters for the initialdesign the cost results and hydraulic analysis results of theinitial design were first reviewed according to Pseudocode 1the results of this review are listed in Tables 5 and 6 Theequalization of the nodal heads and the economical velocitycorresponding to each pipe diameter are generally used as
The Scientific World Journal 7
Dia
met
er (m
m)
15000
30000
70000
130000
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
If the structure of a water supply system and its con-straints (water pressure and velocity) are known the optimaldesign of thewater supply system can be expressed in terms ofthe selection of a pipe diameter that minimizes the total costThe mathematical optimization methods described earliercan easily be used to find the optimal solutions in smallsystems within an ideal environment
However if existing mathematical optimization methodsare applied to actual civil engineering problems the limita-tions of these methods are revealed For example in linearprogramming because all functions applied to such problemsare linear simplified assumptions lower the accuracy of thefinal solution On the other hand in dynamic programmingtoo many combinations have to be considered to obtain theoptimal solutions thereby requiring a considerable amountof computational effort and storage space
In nonlinear programming if the initial solution is notlocated at a good position within the solution zone the globaloptimum is unobtainable and the initial solution cannotescape from the local optima To overcome these disadvan-tages during the last 20 years researchers have attempted toapply new approaches to optimization technologies that donot use an existing mathematical methodology
Rather than relying completely on conventional differen-tial derivatives the technologies currently being developedapply a natural evolution phenomenon that is the principleof the survival of the fittest and artificial imitations of thisphenomena in the optimal system design these have yieldedbetter results than those obtained using an existing optimalmathematical design
Such nature-inspired optimization algorithms are calledmetaheuristic algorithms Some examples of such algorithmsinclude a Genetic Algorithm (GA) Simulated Annealing(SA) Tabu Search (TS) Ant Colony Optimization (ACO)Harmony Search (HS) and Particle Swarm Optimization(PSO) Reca et al [7] Monem and Namdarian [8] daConceicao Cunha and Ribeiro [9] Zecchin et al [10] Geemet al [11] and Montalvo et al [12] have conducted studieson the optimal design of water supply systems using the GASA TS ACOHS and PSO algorithms respectively In recentyears hybrid versions of existing algorithms and new algo-rithms have been also developed such as Genetic HeritageEvolution by Stochastic Transmission (GHEST [13]) NLP-Differential Evolution algorithm (Combined NLP-DE [14])Hybrid Particle Swarm Optimization and Differential Evo-lution (Hybrid PSO-DE [15]) and Charged System Searchalgorithm (CSS [16])
However most of these studies have disadvantages in thatthey were applied to small benchmark problems and werenot reflected in the actual plans [17] The present study aimsto develop an optimal pipe diameter estimation technique ofan actual agricultural looped irrigation water supply systemusing an HS algorithm This study has two main purposesThe first is to develop an economic pipe diameter estimationalgorithm and programusing the optimization techniques foragricultural irrigation water supply systems The second isto validate the developed program by applying the proposedoptimized economic pipe diameter to an actual target region(Saemangeum business area zone 6)
Table 1 Land use divisions according to the comprehensive Sae-mangeum development plan
The Saemangeum Project is a reclamation project intendedto create land from a mud flat and sea waters along thewestern coast of South Korea by constructing a 339 km longseawall Under the Saemangeum Project which was startedon November 16 1991 the construction of a cofferdam wascompleted on April 21 2006 and the reinforcement andembankment projects were completed on April 27 2010
TheSaemangeumseawall is listed in theGuinness Book ofWorld Records as the longest seawall on record and is 14 kmlonger than the Zuider seawall (325 km) of the Netherlandswhichwas earlier regarded to be the longestThe constructionof the seawall has resulted in the reclamation of a new regionwith an area of 401 km2 of which land and a fresh water lakeaccount for 283 km2 and 118 km2 respectively
Upon completion of the seawall construction the SouthKorean Government newly formulated its ComprehensiveSaemangeum Development Plan According to this plan thereclaimed land is to be developed as the central agriculturaland economic sector of Northeast Asia with the reclaimedland mainly divided into nine areas as shown in Figure 1 andTable 1
Agricultural lands account for the largest share (303)among the divided areas These agricultural lands are usedfor ensuring national competitiveness producing high-value-added agricultural products and developing food-industryfacilities through mixed environment-friendly agricultureand ecological crop cultivation Traditionally agriculturalirrigation water supply systems have been designed asbranched water supply networks which incur less initialcosts However such networks are disadvantageous in thatthey do not ensure the reliability of the water supply
In recent years new cultivation methods such as green-house crop cultivation high-value-added crop cultivationand perennial cultivation have been adopted Accordinglyagricultural irrigation water supply systems also need to pro-vide a stable and reliable water supply as achieved by urbanwater supply systems
Figure 1 Comprehensive Saemangeum development plan
3 Model Development and Methodology
31 Harmony Search Algorithm The HS algorithm proposedby Geem et al [11] is an optimization technique used in pipedesign HS is a solution-finding technique that considers anoptimal solution in engineering to correspond to an optimalsound in music Generally heuristic search methods involvethe observation of natural phenomena but the HS method isan algorithmbased on the artificial phenomenon of harmony
When sounds are produced by various sources theytogether create a single harmony Some of these createdharmonies sound pleasant whereas others sound dissonantEventually the discordant harmonies disappear throughpractice and among the more appropriate harmonies (localoptimum) those that are aesthetically the most beautiful(global optimum) are achieved
In other words the HS algorithm considers an optimalsolution to be an optimal harmony found through practiceThe principle of the HS algorithm can be explained indetail by first comparing how music improvisation andoptimization calculations correspond to each other
Improvisation is the spontaneous creation of notes byperformers without relying on sheet music (score) Theability of the performers improves the more they performtogether and ultimately a top-level harmony is created Insuch an improvisation each performer (eg a saxophonistguitarist and double bass player as shown in Figure 2) canbe referred to as a decision variable or design variable (120594
1 1205942
and 1205943in Figure 2)
The musical range of each instrument (in the case of thesaxophonist eg one of the notes among Do Re and Mi
can be created) made by the corresponding performer canbe referred to as the range of each variable (in the case of 120594
1
in Figure 2 its pipe diameter may be 100 200 or 300mm)Moreover when each performer plays a different note theharmony they create (eg the harmony in the figure) (iesaxophone Do double bass Mi and guitar Sol) correspondsto the overall solution vector obtained (the solution vector forFigure 2 is 120594
1= 100mm 120594
2= 300mm and 120594
3= 500mm)
by substituting the value of each variableWhether the harmony played at a point in time is of
high quality is judged aesthetically by the performers oraudience through auditory stimuli If the harmony is verypleasant for the performers or audience it will often bereplayed in the memories Likewise during an optimizationwhether a solution vector is good or bad can be determined bysubstituting the vector in an objective function if this yieldsa better functional value than the existing one the solutionvector will be preserved
Moreover in an improvisation as the performance isrepeated better harmonies are created and ultimately ahigh level of ability is reached likewise in an optimizationoperation as additional iterations are carried out betterfunctional values are increasingly developed and ultimatelythe optimum value is obtained
The harmony memory (HM) harmony memory con-sidering rate (HMCR) and pitch adjustment rate (PAR)are important factors in the HS method for finding anoptimal solution First each musical performer should havea memory space to preserve a good harmony before startingthe important process of the HS algorithm a harmony
4 The Scientific World Journal
bullbullbull
bullbullbull
bullbullbull
100mm200mm300mm
300mm400mm500mm
500mm600mm700mm
Do Re Mi Mi Fa Sol Sol La Si
x1 x2 x3
f(100 300 500)
Figure 2 Concepts of a harmony search
BeginObjective function 119891(119909) 119909 = (119909
1 1199092 119909
119889)119879
Generate initial harmonics (Define Harmony Memory and Size HM amp HMS)Define pitch adjusting rate (PAR) pitch limits and bandwidth (BW)Define harmony memory considering rate (HMCR)while (119905 lt 119872119886119909 number of iterations)Generate new harmonics by accepting best harmonicsAdjust pitch to get new harmonics (solutions)if (119903119886119899119889 gt 119867119872119862119877) choose an existing harmonic randomlyelse if (119903119886119899119889 gt 119875119860119877) adjust the pitch randomly within limitselse generate new harmonics via randomizationend ifAccept the new harmonics (solutions) if betterend whileFind the current best solutionsEnd
Pseudocode 1 Pseudocode of HS
memory space is created by consolidating existing memoryspaces
This is called the HM and the maximum number ofharmonies that can be stored in this storage space is calledthe harmony memory size (HMS) Next to produce bettersolutions from the harmony storage space which is initiallyfilled by as many random vectors as the HMS the HSalgorithm employs three types of operators
311 Random Selection In the random selection techniquethe value of a variable is randomly selected from all values ofthe playable note range If119870 is the total number of all possiblevariable values one of them is randomly selected and theprobability of this technique being adopted is 1-HMCR
312 Memory Consideration The memory considerationtechnique picks the value of a variable from the existing high-quality notes In other words a single value is picked fromall values possessed by a variable within the storage space
Its probability is HMCR and although it can have a valuebetween 0 and 1 a value between 07 and 095 is usually usednevertheless the value is changeable
313 Pitch Adjustment For a pitch adjustment a noteobtained through a memory recall technique is considereda basic note and its pitch is trimmed by adjusting the notebased on the surrounding upper and lower notes In an actualcalculation when a single value is obtained using a memoryrecall technique it is adjusted by a one-step higher or lowervalue The PAR is the probability of this technique actuallybeing applied and it can attain a value between 0 and 1Generally the PAR has a value of around 001 to 03 butthis can vary Pseudocode 1 shows the pseudocode of the HSalgorithm
32 Objective Function An objective functionminimizes thedesign cost of an irrigation system The algorithm devel-oped in the present study was applied to an optimization
The Scientific World Journal 5
Figure 3 A looped water supply network applied to the target zone of Saemangeum
the construction costs pipe material costs and maintenancecosts are considered as the design costs according to the pipediameterTherefore the equation for the objective function isas follows
where 119862119862(119863119894) is cost function (construction cost) per unit
length (m) for each pipe diameter 119862119872(119863119894) is cost function
(maintenance cost) per unit length (m) for each pipe diam-eter 119862
119875(119863119894) is cost function (pipe material cost) per unit
length (m) for each pipe diameter 119871119894is length of the pipe (m)
119863119894is pipe diameter (mm) and119873 is total number of pipesHydraulic constraint equations are considered in opti-
mization problems Therefore a penalty function method isintroduced to convert the optimization problem subject toconstraint conditions into an optimization that is free fromthe constraint conditionsThe final objective function whichis applied using a penalty function can be defined as follows
10038161003816100381610038161003816ℎ119895minus ℎmin or max
10038161003816100381610038161003816
+
119873
sum
119894=1
119875119894
1003816100381610038161003816V119894 minus Vmin or max1003816100381610038161003816
(2)
where ℎ119895is pressure head of each node (m) ℎmin is minimum
pressure head (m) ℎmax is maximum pressure head (m) V119894
is velocity of each pipe (ms) Vmin is minimum pipe velocity(ms) Vmax is maximum pipe velocity (ms) 119875
119895 119875119894are penalty
functionswith regard to the pressure and pipe velocity and119872is total number of nodes
The above penalty function is applied only when thepressure of each node and the velocity of the pipe exceedeither the minimum or maximum value the equation belowrepresents the penalty function equation applied to the
present model In the target water supply system the mini-mum and maximum nodal pressures were set to 10 and 35mrespectively and the minimum andmaximum pipe velocitieswere set to 001 and 25ms respectively
119875119895= 120572 (10038161003816100381610038161003816ℎ119895minus ℎmin or ℎmax minus ℎ119895
10038161003816100381610038161003816) + 120573
119875119894= 120572 (1003816100381610038161003816V119894 minus Vmin or Vmax minus V119894
1003816100381610038161003816) + 120573
(3)
where 120572 120573 are penalty constantsWhen running an optimization model if the pressure
head of each node and the velocity of the pipe do notsatisfy the minimum and maximum values which are thedesign conditions the penalty cost is increased by assigninga significantly greater value to 120572 so that the solution willnot be selected To prepare for a case in which the pressurehead and pipe velocity fall short of the design conditions bya small margin a model that largely satisfies all of the designconditions was implemented by assigning a large value to 120573A trial-and-error analysis was conducted using the 120572 and 120573values for Saemangeumwhich is the target area of the presentproject The results indicate that an effective optimal designis possible when 120572 and 120573 are assigned values of 10000000and 100000000 respectively But detailed studies aboutconstraint handling techniques and determination of theirparameters should be tackled to improve model efficiencyand reliability in future
4 Saemangeum Water Supply NetworkApplication and Results
41 Target Water Supply Network In the present studyproposal data on the loop-type design of the six zones ofSaemangeum were obtained and applied to one of the zonesA diagram of the corresponding water supply network isshown in Figure 3The targetwater supply network comprises356 pipelines and as mentioned earlier some of the networkconsists of a circuit-type water supply
The data on the cost incurred per unit of pipe length forthe different diameter pipes used in this study are listed inTable 2 For optimization 18 types of commercial pipes with
6 The Scientific World Journal
Table 2 Cost data corresponding to different pipe diameters for Saemangeum
Pipe diameter (mm) Cost (xm)Construction costs Material costs Maintenance costs
Table 3 Decision variables and number of possible solutions for the target water supply network
Target water supply network Number of water supply networkdecision variables in the initial design Total length of the pipeline Number of
possible solutionsSix zones of Saemangeum(loop type) 356 40440m 18356 ≒ infin
different diameters were considered Data on the construc-tion and pipe material costs corresponding to the differentpipe diameters were obtained from the ldquoWater FacilitiesConstruction Cost Estimation Reportrdquo from K-water [18]which provides estimated data on the construction costs fordifferent steel pipe diameters The task of optimization wascarried out on Intel(R) Core(TM) i5-3570 CPU at 34GHzwith 4GBRAM EPANET [1] was used as a hydraulic analysisprogram
42 Parameter Settings The number of decision variableswhich should be determined through optimization is 356because there are 356 pipelines in the target water supplynetwork As indicated in Table 2 18 pipe diameters wereconsidered for the target water supply network Hence thenumber of possible solutions that can be considered duringthe design period is infinite as mentioned in Table 3
The parameters applied in the present program forthe Saemangeum target water supply network are listed inTable 4 The size of the harmony memory (HMS) the valueof the HMCR parameter and the value of PAR were set to 30097 and 001 respectively
These values which correspond to the optimum resultsare adjusted therefore the convergence time and efficiencyof the optimal solution vary However when there are many
Table 4 Cost data based on pipe diameters as applied to Saeman-geum
Control parameters Set valueHMS 30HMCR 097PAR 001Constraint condition (pressure ℎ) 10 lt ℎ lt 35
Constraint condition (pipe velocity V) 001 lt V lt 25
decision variables and in such a case if large HMCR andsmall PAR values are used the efficiency of the optimizationgenerally increases
43 The Economic Feasibility of the Initial Design andHydraulic Analysis Evaluation To compare and evaluate theoptimization results of the pipe diameters for the initialdesign the cost results and hydraulic analysis results of theinitial design were first reviewed according to Pseudocode 1the results of this review are listed in Tables 5 and 6 Theequalization of the nodal heads and the economical velocitycorresponding to each pipe diameter are generally used as
The Scientific World Journal 7
Dia
met
er (m
m)
15000
30000
70000
130000
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
Figure 1 Comprehensive Saemangeum development plan
3 Model Development and Methodology
31 Harmony Search Algorithm The HS algorithm proposedby Geem et al [11] is an optimization technique used in pipedesign HS is a solution-finding technique that considers anoptimal solution in engineering to correspond to an optimalsound in music Generally heuristic search methods involvethe observation of natural phenomena but the HS method isan algorithmbased on the artificial phenomenon of harmony
When sounds are produced by various sources theytogether create a single harmony Some of these createdharmonies sound pleasant whereas others sound dissonantEventually the discordant harmonies disappear throughpractice and among the more appropriate harmonies (localoptimum) those that are aesthetically the most beautiful(global optimum) are achieved
In other words the HS algorithm considers an optimalsolution to be an optimal harmony found through practiceThe principle of the HS algorithm can be explained indetail by first comparing how music improvisation andoptimization calculations correspond to each other
Improvisation is the spontaneous creation of notes byperformers without relying on sheet music (score) Theability of the performers improves the more they performtogether and ultimately a top-level harmony is created Insuch an improvisation each performer (eg a saxophonistguitarist and double bass player as shown in Figure 2) canbe referred to as a decision variable or design variable (120594
1 1205942
and 1205943in Figure 2)
The musical range of each instrument (in the case of thesaxophonist eg one of the notes among Do Re and Mi
can be created) made by the corresponding performer canbe referred to as the range of each variable (in the case of 120594
1
in Figure 2 its pipe diameter may be 100 200 or 300mm)Moreover when each performer plays a different note theharmony they create (eg the harmony in the figure) (iesaxophone Do double bass Mi and guitar Sol) correspondsto the overall solution vector obtained (the solution vector forFigure 2 is 120594
1= 100mm 120594
2= 300mm and 120594
3= 500mm)
by substituting the value of each variableWhether the harmony played at a point in time is of
high quality is judged aesthetically by the performers oraudience through auditory stimuli If the harmony is verypleasant for the performers or audience it will often bereplayed in the memories Likewise during an optimizationwhether a solution vector is good or bad can be determined bysubstituting the vector in an objective function if this yieldsa better functional value than the existing one the solutionvector will be preserved
Moreover in an improvisation as the performance isrepeated better harmonies are created and ultimately ahigh level of ability is reached likewise in an optimizationoperation as additional iterations are carried out betterfunctional values are increasingly developed and ultimatelythe optimum value is obtained
The harmony memory (HM) harmony memory con-sidering rate (HMCR) and pitch adjustment rate (PAR)are important factors in the HS method for finding anoptimal solution First each musical performer should havea memory space to preserve a good harmony before startingthe important process of the HS algorithm a harmony
4 The Scientific World Journal
bullbullbull
bullbullbull
bullbullbull
100mm200mm300mm
300mm400mm500mm
500mm600mm700mm
Do Re Mi Mi Fa Sol Sol La Si
x1 x2 x3
f(100 300 500)
Figure 2 Concepts of a harmony search
BeginObjective function 119891(119909) 119909 = (119909
1 1199092 119909
119889)119879
Generate initial harmonics (Define Harmony Memory and Size HM amp HMS)Define pitch adjusting rate (PAR) pitch limits and bandwidth (BW)Define harmony memory considering rate (HMCR)while (119905 lt 119872119886119909 number of iterations)Generate new harmonics by accepting best harmonicsAdjust pitch to get new harmonics (solutions)if (119903119886119899119889 gt 119867119872119862119877) choose an existing harmonic randomlyelse if (119903119886119899119889 gt 119875119860119877) adjust the pitch randomly within limitselse generate new harmonics via randomizationend ifAccept the new harmonics (solutions) if betterend whileFind the current best solutionsEnd
Pseudocode 1 Pseudocode of HS
memory space is created by consolidating existing memoryspaces
This is called the HM and the maximum number ofharmonies that can be stored in this storage space is calledthe harmony memory size (HMS) Next to produce bettersolutions from the harmony storage space which is initiallyfilled by as many random vectors as the HMS the HSalgorithm employs three types of operators
311 Random Selection In the random selection techniquethe value of a variable is randomly selected from all values ofthe playable note range If119870 is the total number of all possiblevariable values one of them is randomly selected and theprobability of this technique being adopted is 1-HMCR
312 Memory Consideration The memory considerationtechnique picks the value of a variable from the existing high-quality notes In other words a single value is picked fromall values possessed by a variable within the storage space
Its probability is HMCR and although it can have a valuebetween 0 and 1 a value between 07 and 095 is usually usednevertheless the value is changeable
313 Pitch Adjustment For a pitch adjustment a noteobtained through a memory recall technique is considereda basic note and its pitch is trimmed by adjusting the notebased on the surrounding upper and lower notes In an actualcalculation when a single value is obtained using a memoryrecall technique it is adjusted by a one-step higher or lowervalue The PAR is the probability of this technique actuallybeing applied and it can attain a value between 0 and 1Generally the PAR has a value of around 001 to 03 butthis can vary Pseudocode 1 shows the pseudocode of the HSalgorithm
32 Objective Function An objective functionminimizes thedesign cost of an irrigation system The algorithm devel-oped in the present study was applied to an optimization
The Scientific World Journal 5
Figure 3 A looped water supply network applied to the target zone of Saemangeum
the construction costs pipe material costs and maintenancecosts are considered as the design costs according to the pipediameterTherefore the equation for the objective function isas follows
where 119862119862(119863119894) is cost function (construction cost) per unit
length (m) for each pipe diameter 119862119872(119863119894) is cost function
(maintenance cost) per unit length (m) for each pipe diam-eter 119862
119875(119863119894) is cost function (pipe material cost) per unit
length (m) for each pipe diameter 119871119894is length of the pipe (m)
119863119894is pipe diameter (mm) and119873 is total number of pipesHydraulic constraint equations are considered in opti-
mization problems Therefore a penalty function method isintroduced to convert the optimization problem subject toconstraint conditions into an optimization that is free fromthe constraint conditionsThe final objective function whichis applied using a penalty function can be defined as follows
10038161003816100381610038161003816ℎ119895minus ℎmin or max
10038161003816100381610038161003816
+
119873
sum
119894=1
119875119894
1003816100381610038161003816V119894 minus Vmin or max1003816100381610038161003816
(2)
where ℎ119895is pressure head of each node (m) ℎmin is minimum
pressure head (m) ℎmax is maximum pressure head (m) V119894
is velocity of each pipe (ms) Vmin is minimum pipe velocity(ms) Vmax is maximum pipe velocity (ms) 119875
119895 119875119894are penalty
functionswith regard to the pressure and pipe velocity and119872is total number of nodes
The above penalty function is applied only when thepressure of each node and the velocity of the pipe exceedeither the minimum or maximum value the equation belowrepresents the penalty function equation applied to the
present model In the target water supply system the mini-mum and maximum nodal pressures were set to 10 and 35mrespectively and the minimum andmaximum pipe velocitieswere set to 001 and 25ms respectively
119875119895= 120572 (10038161003816100381610038161003816ℎ119895minus ℎmin or ℎmax minus ℎ119895
10038161003816100381610038161003816) + 120573
119875119894= 120572 (1003816100381610038161003816V119894 minus Vmin or Vmax minus V119894
1003816100381610038161003816) + 120573
(3)
where 120572 120573 are penalty constantsWhen running an optimization model if the pressure
head of each node and the velocity of the pipe do notsatisfy the minimum and maximum values which are thedesign conditions the penalty cost is increased by assigninga significantly greater value to 120572 so that the solution willnot be selected To prepare for a case in which the pressurehead and pipe velocity fall short of the design conditions bya small margin a model that largely satisfies all of the designconditions was implemented by assigning a large value to 120573A trial-and-error analysis was conducted using the 120572 and 120573values for Saemangeumwhich is the target area of the presentproject The results indicate that an effective optimal designis possible when 120572 and 120573 are assigned values of 10000000and 100000000 respectively But detailed studies aboutconstraint handling techniques and determination of theirparameters should be tackled to improve model efficiencyand reliability in future
4 Saemangeum Water Supply NetworkApplication and Results
41 Target Water Supply Network In the present studyproposal data on the loop-type design of the six zones ofSaemangeum were obtained and applied to one of the zonesA diagram of the corresponding water supply network isshown in Figure 3The targetwater supply network comprises356 pipelines and as mentioned earlier some of the networkconsists of a circuit-type water supply
The data on the cost incurred per unit of pipe length forthe different diameter pipes used in this study are listed inTable 2 For optimization 18 types of commercial pipes with
6 The Scientific World Journal
Table 2 Cost data corresponding to different pipe diameters for Saemangeum
Pipe diameter (mm) Cost (xm)Construction costs Material costs Maintenance costs
Table 3 Decision variables and number of possible solutions for the target water supply network
Target water supply network Number of water supply networkdecision variables in the initial design Total length of the pipeline Number of
possible solutionsSix zones of Saemangeum(loop type) 356 40440m 18356 ≒ infin
different diameters were considered Data on the construc-tion and pipe material costs corresponding to the differentpipe diameters were obtained from the ldquoWater FacilitiesConstruction Cost Estimation Reportrdquo from K-water [18]which provides estimated data on the construction costs fordifferent steel pipe diameters The task of optimization wascarried out on Intel(R) Core(TM) i5-3570 CPU at 34GHzwith 4GBRAM EPANET [1] was used as a hydraulic analysisprogram
42 Parameter Settings The number of decision variableswhich should be determined through optimization is 356because there are 356 pipelines in the target water supplynetwork As indicated in Table 2 18 pipe diameters wereconsidered for the target water supply network Hence thenumber of possible solutions that can be considered duringthe design period is infinite as mentioned in Table 3
The parameters applied in the present program forthe Saemangeum target water supply network are listed inTable 4 The size of the harmony memory (HMS) the valueof the HMCR parameter and the value of PAR were set to 30097 and 001 respectively
These values which correspond to the optimum resultsare adjusted therefore the convergence time and efficiencyof the optimal solution vary However when there are many
Table 4 Cost data based on pipe diameters as applied to Saeman-geum
Control parameters Set valueHMS 30HMCR 097PAR 001Constraint condition (pressure ℎ) 10 lt ℎ lt 35
Constraint condition (pipe velocity V) 001 lt V lt 25
decision variables and in such a case if large HMCR andsmall PAR values are used the efficiency of the optimizationgenerally increases
43 The Economic Feasibility of the Initial Design andHydraulic Analysis Evaluation To compare and evaluate theoptimization results of the pipe diameters for the initialdesign the cost results and hydraulic analysis results of theinitial design were first reviewed according to Pseudocode 1the results of this review are listed in Tables 5 and 6 Theequalization of the nodal heads and the economical velocitycorresponding to each pipe diameter are generally used as
The Scientific World Journal 7
Dia
met
er (m
m)
15000
30000
70000
130000
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
BeginObjective function 119891(119909) 119909 = (119909
1 1199092 119909
119889)119879
Generate initial harmonics (Define Harmony Memory and Size HM amp HMS)Define pitch adjusting rate (PAR) pitch limits and bandwidth (BW)Define harmony memory considering rate (HMCR)while (119905 lt 119872119886119909 number of iterations)Generate new harmonics by accepting best harmonicsAdjust pitch to get new harmonics (solutions)if (119903119886119899119889 gt 119867119872119862119877) choose an existing harmonic randomlyelse if (119903119886119899119889 gt 119875119860119877) adjust the pitch randomly within limitselse generate new harmonics via randomizationend ifAccept the new harmonics (solutions) if betterend whileFind the current best solutionsEnd
Pseudocode 1 Pseudocode of HS
memory space is created by consolidating existing memoryspaces
This is called the HM and the maximum number ofharmonies that can be stored in this storage space is calledthe harmony memory size (HMS) Next to produce bettersolutions from the harmony storage space which is initiallyfilled by as many random vectors as the HMS the HSalgorithm employs three types of operators
311 Random Selection In the random selection techniquethe value of a variable is randomly selected from all values ofthe playable note range If119870 is the total number of all possiblevariable values one of them is randomly selected and theprobability of this technique being adopted is 1-HMCR
312 Memory Consideration The memory considerationtechnique picks the value of a variable from the existing high-quality notes In other words a single value is picked fromall values possessed by a variable within the storage space
Its probability is HMCR and although it can have a valuebetween 0 and 1 a value between 07 and 095 is usually usednevertheless the value is changeable
313 Pitch Adjustment For a pitch adjustment a noteobtained through a memory recall technique is considereda basic note and its pitch is trimmed by adjusting the notebased on the surrounding upper and lower notes In an actualcalculation when a single value is obtained using a memoryrecall technique it is adjusted by a one-step higher or lowervalue The PAR is the probability of this technique actuallybeing applied and it can attain a value between 0 and 1Generally the PAR has a value of around 001 to 03 butthis can vary Pseudocode 1 shows the pseudocode of the HSalgorithm
32 Objective Function An objective functionminimizes thedesign cost of an irrigation system The algorithm devel-oped in the present study was applied to an optimization
The Scientific World Journal 5
Figure 3 A looped water supply network applied to the target zone of Saemangeum
the construction costs pipe material costs and maintenancecosts are considered as the design costs according to the pipediameterTherefore the equation for the objective function isas follows
where 119862119862(119863119894) is cost function (construction cost) per unit
length (m) for each pipe diameter 119862119872(119863119894) is cost function
(maintenance cost) per unit length (m) for each pipe diam-eter 119862
119875(119863119894) is cost function (pipe material cost) per unit
length (m) for each pipe diameter 119871119894is length of the pipe (m)
119863119894is pipe diameter (mm) and119873 is total number of pipesHydraulic constraint equations are considered in opti-
mization problems Therefore a penalty function method isintroduced to convert the optimization problem subject toconstraint conditions into an optimization that is free fromthe constraint conditionsThe final objective function whichis applied using a penalty function can be defined as follows
10038161003816100381610038161003816ℎ119895minus ℎmin or max
10038161003816100381610038161003816
+
119873
sum
119894=1
119875119894
1003816100381610038161003816V119894 minus Vmin or max1003816100381610038161003816
(2)
where ℎ119895is pressure head of each node (m) ℎmin is minimum
pressure head (m) ℎmax is maximum pressure head (m) V119894
is velocity of each pipe (ms) Vmin is minimum pipe velocity(ms) Vmax is maximum pipe velocity (ms) 119875
119895 119875119894are penalty
functionswith regard to the pressure and pipe velocity and119872is total number of nodes
The above penalty function is applied only when thepressure of each node and the velocity of the pipe exceedeither the minimum or maximum value the equation belowrepresents the penalty function equation applied to the
present model In the target water supply system the mini-mum and maximum nodal pressures were set to 10 and 35mrespectively and the minimum andmaximum pipe velocitieswere set to 001 and 25ms respectively
119875119895= 120572 (10038161003816100381610038161003816ℎ119895minus ℎmin or ℎmax minus ℎ119895
10038161003816100381610038161003816) + 120573
119875119894= 120572 (1003816100381610038161003816V119894 minus Vmin or Vmax minus V119894
1003816100381610038161003816) + 120573
(3)
where 120572 120573 are penalty constantsWhen running an optimization model if the pressure
head of each node and the velocity of the pipe do notsatisfy the minimum and maximum values which are thedesign conditions the penalty cost is increased by assigninga significantly greater value to 120572 so that the solution willnot be selected To prepare for a case in which the pressurehead and pipe velocity fall short of the design conditions bya small margin a model that largely satisfies all of the designconditions was implemented by assigning a large value to 120573A trial-and-error analysis was conducted using the 120572 and 120573values for Saemangeumwhich is the target area of the presentproject The results indicate that an effective optimal designis possible when 120572 and 120573 are assigned values of 10000000and 100000000 respectively But detailed studies aboutconstraint handling techniques and determination of theirparameters should be tackled to improve model efficiencyand reliability in future
4 Saemangeum Water Supply NetworkApplication and Results
41 Target Water Supply Network In the present studyproposal data on the loop-type design of the six zones ofSaemangeum were obtained and applied to one of the zonesA diagram of the corresponding water supply network isshown in Figure 3The targetwater supply network comprises356 pipelines and as mentioned earlier some of the networkconsists of a circuit-type water supply
The data on the cost incurred per unit of pipe length forthe different diameter pipes used in this study are listed inTable 2 For optimization 18 types of commercial pipes with
6 The Scientific World Journal
Table 2 Cost data corresponding to different pipe diameters for Saemangeum
Pipe diameter (mm) Cost (xm)Construction costs Material costs Maintenance costs
Table 3 Decision variables and number of possible solutions for the target water supply network
Target water supply network Number of water supply networkdecision variables in the initial design Total length of the pipeline Number of
possible solutionsSix zones of Saemangeum(loop type) 356 40440m 18356 ≒ infin
different diameters were considered Data on the construc-tion and pipe material costs corresponding to the differentpipe diameters were obtained from the ldquoWater FacilitiesConstruction Cost Estimation Reportrdquo from K-water [18]which provides estimated data on the construction costs fordifferent steel pipe diameters The task of optimization wascarried out on Intel(R) Core(TM) i5-3570 CPU at 34GHzwith 4GBRAM EPANET [1] was used as a hydraulic analysisprogram
42 Parameter Settings The number of decision variableswhich should be determined through optimization is 356because there are 356 pipelines in the target water supplynetwork As indicated in Table 2 18 pipe diameters wereconsidered for the target water supply network Hence thenumber of possible solutions that can be considered duringthe design period is infinite as mentioned in Table 3
The parameters applied in the present program forthe Saemangeum target water supply network are listed inTable 4 The size of the harmony memory (HMS) the valueof the HMCR parameter and the value of PAR were set to 30097 and 001 respectively
These values which correspond to the optimum resultsare adjusted therefore the convergence time and efficiencyof the optimal solution vary However when there are many
Table 4 Cost data based on pipe diameters as applied to Saeman-geum
Control parameters Set valueHMS 30HMCR 097PAR 001Constraint condition (pressure ℎ) 10 lt ℎ lt 35
Constraint condition (pipe velocity V) 001 lt V lt 25
decision variables and in such a case if large HMCR andsmall PAR values are used the efficiency of the optimizationgenerally increases
43 The Economic Feasibility of the Initial Design andHydraulic Analysis Evaluation To compare and evaluate theoptimization results of the pipe diameters for the initialdesign the cost results and hydraulic analysis results of theinitial design were first reviewed according to Pseudocode 1the results of this review are listed in Tables 5 and 6 Theequalization of the nodal heads and the economical velocitycorresponding to each pipe diameter are generally used as
The Scientific World Journal 7
Dia
met
er (m
m)
15000
30000
70000
130000
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
Figure 3 A looped water supply network applied to the target zone of Saemangeum
the construction costs pipe material costs and maintenancecosts are considered as the design costs according to the pipediameterTherefore the equation for the objective function isas follows
where 119862119862(119863119894) is cost function (construction cost) per unit
length (m) for each pipe diameter 119862119872(119863119894) is cost function
(maintenance cost) per unit length (m) for each pipe diam-eter 119862
119875(119863119894) is cost function (pipe material cost) per unit
length (m) for each pipe diameter 119871119894is length of the pipe (m)
119863119894is pipe diameter (mm) and119873 is total number of pipesHydraulic constraint equations are considered in opti-
mization problems Therefore a penalty function method isintroduced to convert the optimization problem subject toconstraint conditions into an optimization that is free fromthe constraint conditionsThe final objective function whichis applied using a penalty function can be defined as follows
10038161003816100381610038161003816ℎ119895minus ℎmin or max
10038161003816100381610038161003816
+
119873
sum
119894=1
119875119894
1003816100381610038161003816V119894 minus Vmin or max1003816100381610038161003816
(2)
where ℎ119895is pressure head of each node (m) ℎmin is minimum
pressure head (m) ℎmax is maximum pressure head (m) V119894
is velocity of each pipe (ms) Vmin is minimum pipe velocity(ms) Vmax is maximum pipe velocity (ms) 119875
119895 119875119894are penalty
functionswith regard to the pressure and pipe velocity and119872is total number of nodes
The above penalty function is applied only when thepressure of each node and the velocity of the pipe exceedeither the minimum or maximum value the equation belowrepresents the penalty function equation applied to the
present model In the target water supply system the mini-mum and maximum nodal pressures were set to 10 and 35mrespectively and the minimum andmaximum pipe velocitieswere set to 001 and 25ms respectively
119875119895= 120572 (10038161003816100381610038161003816ℎ119895minus ℎmin or ℎmax minus ℎ119895
10038161003816100381610038161003816) + 120573
119875119894= 120572 (1003816100381610038161003816V119894 minus Vmin or Vmax minus V119894
1003816100381610038161003816) + 120573
(3)
where 120572 120573 are penalty constantsWhen running an optimization model if the pressure
head of each node and the velocity of the pipe do notsatisfy the minimum and maximum values which are thedesign conditions the penalty cost is increased by assigninga significantly greater value to 120572 so that the solution willnot be selected To prepare for a case in which the pressurehead and pipe velocity fall short of the design conditions bya small margin a model that largely satisfies all of the designconditions was implemented by assigning a large value to 120573A trial-and-error analysis was conducted using the 120572 and 120573values for Saemangeumwhich is the target area of the presentproject The results indicate that an effective optimal designis possible when 120572 and 120573 are assigned values of 10000000and 100000000 respectively But detailed studies aboutconstraint handling techniques and determination of theirparameters should be tackled to improve model efficiencyand reliability in future
4 Saemangeum Water Supply NetworkApplication and Results
41 Target Water Supply Network In the present studyproposal data on the loop-type design of the six zones ofSaemangeum were obtained and applied to one of the zonesA diagram of the corresponding water supply network isshown in Figure 3The targetwater supply network comprises356 pipelines and as mentioned earlier some of the networkconsists of a circuit-type water supply
The data on the cost incurred per unit of pipe length forthe different diameter pipes used in this study are listed inTable 2 For optimization 18 types of commercial pipes with
6 The Scientific World Journal
Table 2 Cost data corresponding to different pipe diameters for Saemangeum
Pipe diameter (mm) Cost (xm)Construction costs Material costs Maintenance costs
Table 3 Decision variables and number of possible solutions for the target water supply network
Target water supply network Number of water supply networkdecision variables in the initial design Total length of the pipeline Number of
possible solutionsSix zones of Saemangeum(loop type) 356 40440m 18356 ≒ infin
different diameters were considered Data on the construc-tion and pipe material costs corresponding to the differentpipe diameters were obtained from the ldquoWater FacilitiesConstruction Cost Estimation Reportrdquo from K-water [18]which provides estimated data on the construction costs fordifferent steel pipe diameters The task of optimization wascarried out on Intel(R) Core(TM) i5-3570 CPU at 34GHzwith 4GBRAM EPANET [1] was used as a hydraulic analysisprogram
42 Parameter Settings The number of decision variableswhich should be determined through optimization is 356because there are 356 pipelines in the target water supplynetwork As indicated in Table 2 18 pipe diameters wereconsidered for the target water supply network Hence thenumber of possible solutions that can be considered duringthe design period is infinite as mentioned in Table 3
The parameters applied in the present program forthe Saemangeum target water supply network are listed inTable 4 The size of the harmony memory (HMS) the valueof the HMCR parameter and the value of PAR were set to 30097 and 001 respectively
These values which correspond to the optimum resultsare adjusted therefore the convergence time and efficiencyof the optimal solution vary However when there are many
Table 4 Cost data based on pipe diameters as applied to Saeman-geum
Control parameters Set valueHMS 30HMCR 097PAR 001Constraint condition (pressure ℎ) 10 lt ℎ lt 35
Constraint condition (pipe velocity V) 001 lt V lt 25
decision variables and in such a case if large HMCR andsmall PAR values are used the efficiency of the optimizationgenerally increases
43 The Economic Feasibility of the Initial Design andHydraulic Analysis Evaluation To compare and evaluate theoptimization results of the pipe diameters for the initialdesign the cost results and hydraulic analysis results of theinitial design were first reviewed according to Pseudocode 1the results of this review are listed in Tables 5 and 6 Theequalization of the nodal heads and the economical velocitycorresponding to each pipe diameter are generally used as
The Scientific World Journal 7
Dia
met
er (m
m)
15000
30000
70000
130000
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
Table 3 Decision variables and number of possible solutions for the target water supply network
Target water supply network Number of water supply networkdecision variables in the initial design Total length of the pipeline Number of
possible solutionsSix zones of Saemangeum(loop type) 356 40440m 18356 ≒ infin
different diameters were considered Data on the construc-tion and pipe material costs corresponding to the differentpipe diameters were obtained from the ldquoWater FacilitiesConstruction Cost Estimation Reportrdquo from K-water [18]which provides estimated data on the construction costs fordifferent steel pipe diameters The task of optimization wascarried out on Intel(R) Core(TM) i5-3570 CPU at 34GHzwith 4GBRAM EPANET [1] was used as a hydraulic analysisprogram
42 Parameter Settings The number of decision variableswhich should be determined through optimization is 356because there are 356 pipelines in the target water supplynetwork As indicated in Table 2 18 pipe diameters wereconsidered for the target water supply network Hence thenumber of possible solutions that can be considered duringthe design period is infinite as mentioned in Table 3
The parameters applied in the present program forthe Saemangeum target water supply network are listed inTable 4 The size of the harmony memory (HMS) the valueof the HMCR parameter and the value of PAR were set to 30097 and 001 respectively
These values which correspond to the optimum resultsare adjusted therefore the convergence time and efficiencyof the optimal solution vary However when there are many
Table 4 Cost data based on pipe diameters as applied to Saeman-geum
Control parameters Set valueHMS 30HMCR 097PAR 001Constraint condition (pressure ℎ) 10 lt ℎ lt 35
Constraint condition (pipe velocity V) 001 lt V lt 25
decision variables and in such a case if large HMCR andsmall PAR values are used the efficiency of the optimizationgenerally increases
43 The Economic Feasibility of the Initial Design andHydraulic Analysis Evaluation To compare and evaluate theoptimization results of the pipe diameters for the initialdesign the cost results and hydraulic analysis results of theinitial design were first reviewed according to Pseudocode 1the results of this review are listed in Tables 5 and 6 Theequalization of the nodal heads and the economical velocitycorresponding to each pipe diameter are generally used as
The Scientific World Journal 7
Dia
met
er (m
m)
15000
30000
70000
130000
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
Figure 4 Pipe diameter optimization results for the six zones of the Saemangeum water supply network
Table 5 Comparisons of the costs incurred upon applying the optimal design versus the initial design
Target water supply network Initial design cost (x) Optimal design cost (x) Variation ()Six zones of Saemangeum (looped type) 11200114720 10182733295 minus908
the factors in evaluating the mathematical stability of anirrigation system
The minimum nodal pressure head is mostly stable at avalue greater than 10m In the present initial design a loopednetwork irrigation system is implemented by installing anadditional pipeline to a branched network system In thiscase the supply path up to the demand node is determinedto be a branched network that is only a single type
However in the initial design because various supplypaths are possible the head loss is slight and a water supplyis possible through the hydraulically satisfied supply pathsa system that is more hydraulically stable than a branchednetwork system that can be implemented Thus becausevarious supply paths are possible in a looped irrigationwater supply system a looped system provides a better watersupply than a branched system during abnormal operatingconditions such as during an irrigation path failure or closure
44 Optimal PipeDiameterDesign Results Thepipe diameterwas optimized by considering the pressure and pipe velocityconstraint conditions and the HS parameters which wereexplained earlier in this study The optimization results froma cost-effective pipe diameter are shown in Figure 4
The statistical values of the nodal pressure head andpipeline velocities which are the results of a hydraulicanalysis based on cost-effective pipe diameter and the optimalcost results are shown in Tables 5 and 6 Overall the pressurehead and pipe velocities were confirmed to be stable and acomparison based on the hydraulic stability and economicfeasibility of the initial design was conducted
The application results indicate that the cost reductionrate of the optimal design was considerably greater (908)than that of the initial design These results were furtheranalyzed from the viewpoint of current practices that do not
employ optimization techniques this analysis indicates thateven without using any optimization technique branchednetwork systems that do not significantly differ from theoptimal designs can be created using the current techniques
However in the case of a looped network system suchas the water supply network applied in this study thedifferences in the results were significant therefore it isnecessary to determine an cost-effective pipe diameter forthe optimization technique based on the results obtainedwhen employing current practices The hydraulic analysisresults indicate that the minimum pressure head (more than10m) was mostly satisfied as observed in the initial designFurthermore the statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity all satisfythe economical pipe velocity requirements
5 Differences from Other Existing Plans
In the present study optimal design reviews of two otherdesign plans in addition to the proposed looped networkdesign plan were conducted These two design plans are ofa branch type and a pump type as shown in Figures 5 and 6respectively
The branch-type water supply network comprises 335pipelines with a total length of 3788 km The pump-typewater supply network comprises 345 pipelines for the watersupplied by the pumping of this irrigation network the entirearea encompassing the six zones was reclassified into fournew areas The total length of the pipelines is approximately4139 km
To compare and evaluate the estimation results for theoptimal pipe diameter of the three water supply networksystems that is the loop type (plan 1) branch type (plan 2)
8 The Scientific World Journal
Table 6 Analysis results of the optimal and initial hydraulic designs (based on statistical values of the nodal head and pipe velocity)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
Six zones of Saemangeum (looped type) 1765 3166 2304 1395 001 192 097 016Optimal design 1000 2908 1536 2368 002 246 118 029
Table 7 Optimal design results and cost comparison of the initial plan (three cases)
Target water supply network Initial design costs (x) Optimal design costs (x) Variation ()Loop type (plan 1) 11200114720 10182733295 minus908Branch type (plan 2) 10484719750 10044962405 minus419Pump type (plan 3) 11503515255 11586379380 +072
Table 8 Analysis results of the optimal and initial hydraulic designs (three cases)
Target water supply network Nodal pressure head (m) Pipe velocity (ms)Min Max Avg Var Min Max Avg Var
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
and pump type (plan 3) the cost results according to the finaloptimum pipe diameter and the pipe diameters of the initialplan of each of the three networks are listed in Table 7
The results indicate that the cost of applying the optimaldesign was at a minimum for plan 2 and at a maximum forplan 3 This is similar to the trends found in the initial planHowever an examination of the varying cost rate shows thatthe cost reduction of the optimal design for plan 2 was 419less than that of the initial plan On the other hand the costincreased by 072 for plan 3 whereas in the case of plan 1 thecost reduction rate was very high (908)The results for plan1 show that the reduction rate between the optimal cost andthe total length of the pipes is inversely proportional whenthe pressure head and velocity conditions remain constantMoreover a looped irrigation system has many nodes andpipes which vary hydraulically because pipes of differentdiameters are used in a pipe system this proves that it isdifficult to design a looped irrigation system economicallywithout using an optimization technique
These results are attributed to the fact that the self-nodalpressure head of the initial version of plan 1 is relativelygreater than that of the initial version of plan 2 Howeverfrom the viewpoint of current practices which do not employoptimization techniques branch-type systems such as plans2 and 3 which do not differ greatly from optimal systemscan be designed by applying current techniques In the caseof a looped network system such as plan 1 the differencesbetween the results corresponding to the initial and optimaldesigns were considerable Therefore based on the results
from current practices it is necessary to determine a cost-effective pipe diameter using an optimization technique
The results of a hydraulic analysis in which the optimalpipe diameters for plans 1 2 and 3were considered are shownin Table 8 The statistical values of the nodal pressure headand pipe velocity indicate that the minimum pressure headallowable pipe velocity and average pipe velocity for all threeplans satisfy the economical pipe velocity requirements Anexamination of the nodal pressure head confirms that theminimum pressure head (10m) is mostly stable in plans 1 and2 as is the case of the initial plan In the case of plan 3 theminimum pressure for the initial plan was very low (05m)however the cost increases if the minimum pressure of theinitial plan (05m) exceeds the minimum pressure standards(10m) during the optimal design process
A comparison of the three optimal design types showsthat plan 2 (branch type) is themost economic optimal designbased only on the criterion of minimum costs Howeverbecause plan 2 does not differ greatly from plan 1 in termsof costs it is necessary to derive the final design results byconsidering the hydraulic and maintenance aspects Plan 1is a case in which a looped network irrigation system isimplemented by installing additional pipelines to plan 2which is a branched system
If the pipelines supplied up to the demand node cor-respond to plan 2 (branch network type) the supply pathis determined to be of only one type However in thecase of plan 1 many supply paths are present the watersupply is made possible through the supply paths which are
The Scientific World Journal 9
Figure 5 Branch-type system
Figure 6 Pump-type system
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
hydraulically satisfactory Therefore plan 1 which is a morehydraulically stable system than plan 2 can be implemented
Thus the supply of a looped irrigation water supplysystem during abnormal situations such as an irrigationpath failure or closure is better than that of a branchedirrigationwater supply systembecause the former has varioussupply paths Unlike plans 1 and 2 plan 3 was designed byreclassifying the target pipeline system into four hydraulicallyindependent sections and water was supplied to each sectionthrough pumping heads By dividing the target pipelinesystem into four hydraulically independent sections thefluctuations in the water quantities by each area can be moreeffectively and reasonably handled and plan 3 can respond tofuture pipeline maintenance and expansion plans Howeverthe increased use of pumps can causemaintenance difficultiesand an increase in maintenance costs
6 Conclusions
In the present study the HS algorithm which is one of thelatest optimization techniques was introduced in the designof an agricultural irrigation system and a correspondingprogramwas developedThe developed programwas appliedto the actual target area (Saemangeum business area zone
6) and the results were presented in this paper Currentlyused methods have disadvantages in that the pipe diameterhas to be adjusted through a hydraulic calculation of thegiven water supply network and this process has to berepeated until satisfactory results are obtained Unlike thiscalculationmethod themodel presented herein yields resultsthat automatically meet the hydraulic conditions through thecombined use of the HS algorithm and a hydraulic analysisHence a comparative analysis is simple and effective Theresults obtained by applying this method to an actual large-scale water supply network are better than those obtainedusing existing mathematical algorithms even after consider-ing the nonlinearity which is inevitable during the analysisThe calculation results of the optimal construction costs andthe pipe diameter when applying the proposed model tothe actual target region (Saemangeum business area zone 6)indicate that the optimal design results obtained using HSyield much better results (9) in terms of cost than thoseof the presently utilized economic pipe diameter calculationtechniques In particular the optimization technique wasfound to be more necessary in the optimal design of a loopednetwork irrigation system than for a branchednetwork irriga-tion system Furthermore an examination of the hydrologicalfactors of a pipeline system in which cost-effective pipe
10 The Scientific World Journal
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
diameters were applied showed that based on the statisticalvalues of the head and pipe velocity the minimum pressurehead the allowable pipe velocity and the average pipe velocityall satisfy the requirements of an economical pipe velocityTherefore if the benefits of the proposed model are proventhrough application in future systems it will show the modelto be a useful decision-making tool for designing loopednetwork water supply systems
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Research Founda-tion of Korean (NRF) Grant funded by the Korean Govern-ment (MSIP) (NRF 2013R1A2A1A01013886)
References
[1] Rossman EPANET 20 Userrsquos Manual EPA 2000[2] BentleyWater GEMS Userrsquos Manual 2007[3] E Alperovits and U Shamir ldquoDesign of optimal water distribu-
tion systemsrdquoWater Resources Research vol 13 no 6 pp 885ndash900 1977
[4] G E Quindry E D Brill and J C Liebman ldquoOptimization ofloopedwater distribution systemsrdquo Journal of the EnvironmentalEngineering Division vol 107 no 4 pp 665ndash679 1981
[5] O Fujiwara and D B Khang ldquoA two-phase decompositionmethod for optimal design of looped water distribution net-worksrdquo Water Resources Research vol 26 no 4 pp 539ndash5491990
[6] G Eiger U Shamir and A Ben-Tal ldquoOptimal design of waterdistribution networksrdquoWater Resources Research vol 30 no 9pp 2637ndash2646 1994
[7] J Reca J Martınez C Gil and R Banos ldquoApplication of severalmeta-heuristic techniques to the optimization of real loopedwater distribution networksrdquoWater ResourcesManagement vol22 no 10 pp 1367ndash1379 2008
[8] M J Monem and R Namdarian ldquoApplication of simulatedannealing (SA) techniques for optimal water distribution inirrigation canalsrdquo Irrigation and Drainage vol 54 no 4 pp365ndash373 2005
[9] M da Conceicao Cunha and L Ribeiro ldquoTabu search algo-rithms for water network optimizationrdquo European Journal ofOperational Research vol 157 no 3 pp 746ndash758 2004
[10] A C Zecchin A R Simpson H R Maier M Leonard A JRoberts and M J Berrisford ldquoApplication of two ant colonyoptimisation algorithms to water distribution system optimisa-tionrdquo Mathematical and Computer Modelling vol 44 no 5-6pp 451ndash468 2006
[11] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001
[12] I Montalvo J Izquierdo R Perez and M M Tung ldquoParticleswarm optimization applied to the design of water supplysystemsrdquo Computers amp Mathematics with Applications vol 56no 3 pp 769ndash776 2008
[13] A Bolognesi C Bragalli A Marchi and S Artina ldquoGeneticheritage evolution by stochastic transmission in the optimaldesign of water distribution networksrdquoAdvances in EngineeringSoftware vol 41 no 5 pp 792ndash801 2010
[14] F Zheng A R Simpson and A C Zecchin ldquoA combined NLP-differential evolution algorithm approach for the optimizationof loopedwater distribution systemsrdquoWater Resources Researchvol 47 no 8 Article IDW08531 2011
[15] A Sedki and D Ouazar ldquoHybrid particle swarm optimizationand differential evolution for optimal design of water distribu-tion systemsrdquo Advanced Engineering Informatics vol 26 no 3pp 582ndash591 2012
[16] R Sheikholeslami A Kaveh A Tahershamsi and S TalataharildquoApplication of charged system search algorithm to waterdistribution networks optimizationrdquo International Journal ofOptimization in Civil Engineering vol 4 no 1 pp 41ndash58 2014
[17] A de Corte andK Sorensen ldquoOptimisation of gravity-fedwaterdistribution network design a critical reviewrdquo European Journalof Operational Research vol 228 no 1 pp 1ndash10 2013
[18] K-Water Water Facilities Construction Cost Estimation ReportK-Water 2010
